On the local and nonlocal Camassa–Holm hierarchies

2005/03/25 by Paolo Casati, Paolo Lorenzoni, G. Ortenzi +1 · 15 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Applied mathematics #Camassa–Holm equation #Integrable system #Mathematical economics #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics

paper · doi:10.1063/1.1888568

published in Journal of Mathematical Physics 46(4) (American Institute of Physics)

openalex publication_date 2005/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

We construct the local and nonlocal conserved densities for the Camassa–Holm equation by solving a suitable Riccati equation. We also define a Kadomtsev–Petviashvili extension for the local Camassa–Holm hierarchy.

Citations

• The Liouville correspondence between the Korteweg—de Vries and the Camassa‐Holm hierarchies
• Euler equations on homogeneous spaces and Virasoro orbits
• Conservation laws of the Camassa–Holm equation
• On the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym equations

Cited by

• Camassa–Holm equation [wikipedia]